Daily Practice · Higher
January 2019 - Higher 5-a-day
Every Higher sheet published in January 2019, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' January 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2019A, B and C are points on a circle with centre O. Angle AOC is 122°. Work out angle ABC, where B is on the major arc.
- 2nd January 20194 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 3rd January 2019A histogram class is 20 units wide and contains 60 values. Work out the frequency density.
- 4th January 2019Work out (64 x 10^11) / (8 x 10^3). Give your answer in standard form.
- 5th January 2019Expand and simplify (x + 4)(x - 3)(x - 4).
- 6th January 2019y is inversely proportional to x. When x = 6, y = 20. Work out y when x = 4.
- 7th January 2019A cone has base radius 3 cm and vertical height 24 cm. Work out its volume, leaving your answer in terms of pi.
- 8th January 201928 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 9th January 2019Four classes in order have frequencies 10, 9, 6, 8. Write down the cumulative frequency at the end of the third class.
- 10th January 2019Write the recurring decimal 0.444... as a fraction in its simplest form.
- 11th January 2019Make x the subject of y = 2x^2 - 10.
- 12th January 2019y is directly proportional to x^2. When x = 4, y = 144. Work out y when x = 7.
- 13th January 2019In triangle ABC, angle A is 51°, angle B is 90° and side a is 19 cm. Use the sine rule to work out side b, to 1 decimal place.
- 14th January 20192 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 15th January 201915 voles are marked and released. Later 96 are caught, of which 8 are marked. Estimate the population.
- 16th January 2019Work out 25^(3/2).
- 17th January 2019Factorise x^2 - 81.
- 18th January 2019y is directly proportional to x. When x = 3, y = 27. Work out y when x = 2.
- 19th January 2019A right-angled triangle has sides 8 cm, 15 cm and 17 cm. Work out the angle opposite the 8 cm side, to 1 decimal place.
- 20th January 201925 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 21st January 2019A cumulative frequency graph is drawn for 84 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 22nd January 2019Write sqrt(20) in the form a sqrt(b), where b is as small as possible.
- 23rd January 2019A region is defined by y < -x + 7. Should the boundary line be solid or dashed, and why?
- 24th January 2019A town's population is 31500 and grows by 4% each year. Work out the population after 4 years, to the nearest whole number.
- 25th January 2019The point (-1, 3) is enlarged by scale factor -1 about the centre (3, 3). Write down the coordinates of the image.
- 26th January 20191 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 27th January 2019A box plot has a minimum of 4 and a maximum of 41. Work out the range.
- 28th January 2019A meal deal has 4 mains, 7 sides and 4 drinks. How many different meals are possible?
- 29th January 2019Factorise x^2 + 10x + 21.
- 30th January 2019A block has volume 160 cm^3 and density 8 g/cm^3. Work out its mass.
- 31st January 2019Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 351 cm^3. Work out the volume of the smaller.